IRR Calculator — the rate your cash flows actually earn

How it works

NPV falls steadily as the discount rate rises, so the rate where it crosses zero is found by bisection — the same search the interest-rate calculator uses on loans, applied to arbitrary annual flows. The sweep shows the curve the answer sits on: NPV at 0% through 20%, positive below the IRR and negative above it. Two honest boundaries: flows that never change sign against the outlay have no IRR at all (nothing to solve — the page says so rather than inventing a number), and flows that change sign more than once can admit multiple mathematically valid rates, where the NPV-at-hurdle view is the safer instrument. The hurdle input keeps that view on-page: your required rate, applied to the same flows.

Worked example

The anchor is a published growth pair read as an investment: paying $3,000 today for a single $3,932.39 payoff in year four is exactly the $3,000 → $3,932.39 compound pair (LibreTexts) — so the solver recovers 7.00%, the rate the textbook grew it at, and that is this page's default. CFI's annuity case inverts the same way: paying the $61,446 it says ten $10,000 flows are worth recovers the 10% it was discounted at. Both are the search landing on published arithmetic.

Frequently asked questions

What does the IRR tell me?

The constant annual rate the investment's own cash flows imply — the return the money actually earns if the flows arrive as entered. Comparing it to your hurdle rate answers the same question NPV answers in dollars: above the hurdle and the NPV is positive, below and it is negative.

Why can't IRR be computed directly?

Because the rate appears inside every discount factor — the equation is a polynomial in (1+r) with no general closed form past a few flows. The bisection search converges to machine precision regardless, which the round-trip tests assert.

When does no IRR exist?

When the flows never change sign against the outlay: all gains and nothing paid, or all costs and nothing back. There is no rate at which such flows net to zero, and this page reports that honestly instead of forcing a number.

Can there be more than one IRR?

Yes — flows that flip sign more than once (invest, harvest, then a big cleanup cost) can cross zero at several rates. This page's search returns one crossing; for sign-switching projects, read the NPV sweep instead — the whole curve is unambiguous even when the single-rate summary is not.

How is IRR different from CAGR?

CAGR handles exactly two numbers — start and end — while IRR digests any pattern of flows in between. For a single outlay and a single exit they coincide, which the default case shows: a one-flow IRR IS the pair's CAGR.

Should I decide with IRR or NPV?

They agree on accept/reject against a hurdle for conventional flows; they can rank competing projects differently, because IRR ignores scale — a tiny project with a high rate can beat a large one worth more in dollars. The npv calculator prices the dollar view of the same five flows.

How accurate is this, and what does it exclude?

The solve is exact to machine precision for the flows entered; the uncertainty is the flows themselves. It excludes reinvestment assumptions (IRR implicitly reinvests at itself — optimistic for high rates), mid-year timing, taxes, and risk. Five annual slots bound the horizon, as on the npv page.